Random Matrix Theory with an External Source
This is a first book to show that the theory of the Gaussian random matrix is essential to understand the universal correlations with random fluctuations and to demonstrate that it is useful to evaluate topological universal quantities. We consider Gaussi
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Edouard Brézin Shinobu Hikami
Random Matrix Theory with an External Source
123
SpringerBriefs in Mathematical Physics Volume 19
Series editors Nathanaël Berestycki, Cambridge, UK Mihalis Dafermos, Cambridge, UK Tohru Eguchi, Tokyo, Japan Atsuo Kuniba, Tokyo, Japan Matilde Marcolli, Pasadena, USA Bruno Nachtergaele, Davis, USA
More information about this series at http://www.springer.com/series/11953
Edouard Brézin Shinobu Hikami •
Random Matrix Theory with an External Source
123
Edouard Brézin Laboratoire de Physique Théorique École Normale Supérieure Paris France
Shinobu Hikami Mathematical and Theoretical Physics Unit Okinawa Institute of Science and Technology Graduate University Kunigami-gun, Okinawa Japan
ISSN 2197-1757 ISSN 2197-1765 (electronic) SpringerBriefs in Mathematical Physics ISBN 978-981-10-3315-5 ISBN 978-981-10-3316-2 (eBook) DOI 10.1007/978-981-10-3316-2 Library of Congress Control Number: 2016961269 © The Author(s) 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #22-06/08 Gateway East, Singapore 189721, Singapore
Preface
Random matrix theory (RMT) has a long history, starting with the statistics of nuclear energy levels by Wigner, and it has found applications in wide areas of all sciences from mathematics to biology. The universality of properties derived from random matrices has led to a large number of applications such as network statistics, big data analysis, and biological information. Useful surveys maybe found in [61, 97, 111, 117, 124]. This book deals with Gaussian random matrix models with an external deterministic matrix source. There are also numerous reasons to consider such extensions of standard RMT theory. For insta
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